Paper Reference. Mathematics (Linear) 1380 Paper 3 (Non-Calculator) Higher Tier Thursday 5 November 2009 Morning Time: 1 hour 45 minutes

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1 Centre No. Candidate No. Paper Reference H Surname Signature Paper Reference(s) 1380/3H Edexcel GCSE Mathematics (Linear) 1380 Paper 3 (Non-Calculator) Higher Tier Thursday 5 November 2009 Morning Time: 1 hour 45 minutes Initial(s) Examiner s use only Team Leader s use only Materials required for examination Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used. Items included with question papers Nil Instructions to Candidates In the boxes above, write your centre number, candidate number, your surname, initials and signature. Check that you have the correct question paper. Answer ALL the questions. Write your answers in the spaces provided in this question paper. You must NOT write on the formulae page. Anything you write on the formulae page will gain NO credit. If you need more space to complete your answer to any question, use additional answer sheets. Information for Candidates The marks for individual questions and the parts of questions are shown in round brackets: e.g.. There are 25 questions in this question paper. The total mark for this paper is 100. There are 24 pages in this question paper. Any pages are indicated. Calculators must not be used. Advice to Candidates Show all stages in any calculations. Work steadily through the paper. Do not spend too long on one question. If you cannot answer a question, leave it and attempt the next one. Return at the end to those you have left out. This publication may be reproduced only in accordance with Edexcel Limited copyright policy Edexcel Limited. Printer s Log. No. N35520A W850/R1380/ /6/6/3 *N35520A0124* Turn over

2 GCSE Mathematics (Linear) 1380 Formulae: Higher Tier You must not write on this formulae page. Anything you write on this formulae page will gain NO credit. Volume of a prism = area of cross section length cross section length 4 3 Volume of sphere = πr 3 Volume of cone = πr 2 h Surface area of sphere =4πr 2 Curved surface area of cone = πrl 1 3 r l h r In any triangle ABC C b A c a B The Quadratic Equation The solutions of ax 2 + bx + c =0 where a 0, are given by b± b ac x = 2a 2 ( 4 ) Sine Rule a = b = c sin A sin B sin C Cosine Rule a 2 = b 2 + c 2 2bc cos A Area of triangle = 1 2 ab sin C 2 *N35520A0224*

3 Answer ALL TWENTY FIVE questions. Write your answers in the spaces provided. You must write down all stages in your working. You must NOT use a calculator. 1. Using the information that = write down the value of (a) (1) (b) (1) Q1 (Total 2 marks) 2. Work out an estimate for the value of Q2 (Total 3 marks) *N35520A0324* 3 Turn over

4 3. (a) Complete the table of values for y = 2x + 2 x y 0 2 (b) On the grid, draw the graph of y = 2x + 2 y O x (c) Use your graph to find (i) the value of y when x = 1.5 y =... (ii) the value of x when y = 7 x =... (Total 6 marks) Q3 4 *N35520A0424*

5 4. P Triangle P has been drawn on a grid. (a) On the grid, draw an enlargement of the triangle P with scale factor 3 y Q O x Triangle Q has been drawn on a grid. (b) On the grid, rotate triangle Q 90 clockwise, centre O. (3) Q4 (Total 5 marks) *N35520A0524* 5 Turn over

6 5. Here are the weights in grams, to the nearest gram, of 15 eggs (a) Complete the ordered stem and leaf diagram to show this information. You must include a key. Key (3) Meg is going to pick at random one of the eggs. (b) Work out the probability that this egg will have a weight of more than 45 grams.... Q5 (Total 5 marks) 6 *N35520A0624*

7 6. 30 students took a test. The table shows information about how long it took them to complete the test. Time (t minutes) Frequency 0 < t < t < t < t < t 50 4 (a) On the grid, draw a frequency polygon for this information Frequency O Time (t minutes) (b) Write down the modal class interval.... (1) Q6 (Total 3 marks) *N35520A0724* 7 Turn over

8 7. (a) Work out Give your answer in its simplest form. (b) Work out (c) Work out You must show all your working.... (3) Q7 (Total 7 marks) 8 *N35520A0824*

9 8. Simon wants to find out how much people spend using their mobile phone. He uses this question on a questionnaire. How much do you spend using your mobile phone? (a) Write down two things that are wrong with this question (b) Design a better question for his questionnaire to find out how much people spend using their mobile phone. You should include some response boxes. (Total 4 marks) Q8 *N35520A0924* 9 Turn over

10 9. (a) A solid cube has sides of length 5 cm. Diagram NOT accurately drawn 5 cm 5 cm 5 cm Work out the total surface area of the cube. State the units of your answer. The volume of the cube is 125 cm 3. (b) Change 125 cm 3 into mm (4)... mm 3 The weight of the cube is 87 grams, correct to the nearest gram. (c) (i) What is the minimum the weight could be? (ii) What is the maximum the weight could be?... grams... grams (Total 8 marks) Q9 10 *N35520A01024*

11 10. (a) Simplify 3a + 4c a + 3c... (b) Expand y(2y 3)... (1) (c) Factorise x 2 4x... (d) Expand and simplify 2(x + 3) + 3(2x 1)... (e) Solve 3(x + 2) = 8 x =... Q10 (Total 9 marks) *N35520A01124* 11 Turn over

12 11. The diagram shows the positions of two telephone masts, A and B, on a map. N N B A (a) Measure the bearing of B from A.... (1) Another mast C is on a bearing of 160 from B. On the map, C is 4 cm from B. (b) Mark the position of C with a cross ( ) and label it C. Q11 (Total 3 marks) 12 *N35520A01224*

13 12. Batteries are sold in packets and boxes. Each packet contains 4 batteries. Each box contains 20 batteries. Bill buys p packets of batteries and b boxes of batteries. Bill buys a total of N batteries. 20 BATTERIES Write down a formula for N in terms of p and b.... Q12 (Total 3 marks) 13. (a) Write in standard form (1) (b) Write in standard form (1) Q13 (Total 2 marks) 14. (a) Write down the value of (1) (b) Write down the value of (1) Q14 (Total 2 marks) *N35520A01324* 13 Turn over

14 15. k is an integer such that 1 k < 3 (a) List all the possible values of k.... (b) Solve the inequality 6y y Q15 (Total 4 marks) 16. Make q the subject of the formula 5(q + p) = 4 + 8p Give your answer in its simplest form. q =... Q16 (Total 3 marks) 14 *N35520A01424*

15 17. The box plots show the distribution of marks in an English test and in a Maths test for a group of students. English Maths Marks (a) What is the highest mark in the English test?... (1) (b) Compare the distributions of the marks in the English test and marks in the Maths test Q17 (Total 3 marks) *N35520A01524* 15 Turn over

16 18. A D Diagram NOT accurately drawn E B 35 O B, D and E are points on a circle centre O. ABC is a tangent to the circle. BE is a diameter of the circle. Angle DBE = 35. (a) Find the size of angle ABD. Give a reason for your answer. C... (b) Find the size of angle DEB. Give a reason for your answer.... Q18 (Total 4 marks) 16 *N35520A01624*

17 19. Emma has 7 pens in a box. 5 of the pens are blue. 2 of the pens are red. Emma takes at random a pen from the box and writes down its colour. Emma puts the pen back in the box. Then Emma takes at random a second pen from the box, and writes down its colour. (a) Complete the probability tree diagram. First pen Second pen... Blue... Blue... Red... Blue... Red... Red (b) Work out the probability that Emma takes exactly one pen of each colour from the box.... (3) Q19 (Total 5 marks) *N35520A01724* 17 Turn over

18 20. Solve the simultaneous equations 4x + y = 1 4x 3y = 7 x =... y =... (Total 3 marks) Q Work out (2 + 3)(2 3) Give your answer in its simplest form.... Q21 (Total 2 marks) 18 *N35520A01824*

19 22. a A P Diagram NOT accurately drawn O OAB is a triangle. OA = a, OB = b (a) Find the vector AB b in terms of a and b. B AB =... (1) P is the point on AB so that AP : PB = 2 : 1 (b) Find the vector OP in terms of a and b. Give your answer in its simplest form. OP =... (3) Q22 (Total 4 marks) *N35520A01924* 19 Turn over

20 4 23. Prove that the recurring decimal 036. = 11 Q23 (Total 3 marks) 24. This is a sketch of the curve with the equation y = f(x). The only minimum point of the curve is at P(3, 4). y y = f(x) O x P(3, 4) (a) Write down the coordinates of the minimum point of the curve with the equation y = f(x 2) (...,...) (b) Write down the coordinates of the minimum point of the curve with the equation y = f(x + 5) + 6 (...,...) Q24 (Total 4 marks) 20 *N35520A02024*

21 25. Prove, using algebra, that the sum of two consecutive whole numbers is always an odd number. Q25 END (Total 3 marks) TOTAL FOR PAPER: 100 MARKS *N35520A02124* 21

22 BLANK PAGE 22 *N35520A02224*

23 BLANK PAGE *N35520A02324* 23

24 BLANK PAGE 24 *N35520A02424*

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